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Which of the following is the group of derived units?A.m,s,Pa  𝑎𝑛𝑑  Nm,s,PaandNB.Pa,N,m/s  𝑎𝑛𝑑  WPa,N,m/sandWC.k,m,kgk,m,kg and ssD.kg,K,Pa  𝑎𝑛𝑑  Nkg,K,PaandN

Question

Which of the following is the group of derived units?

A. m, s, Pa  𝑎𝑛𝑑  Nm, s, Pa and N
B. Pa, N, m/s  𝑎𝑛𝑑  W
C. k, m, kg k, m, kg and s
D. kg, K, Pa  𝑎𝑛𝑑  N kg, K, Pa and N

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Solution

The derived units are combinations of the seven base units from the International System of Units (SI). These base units are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).

Let's analyze each option:

A. m (meter), s (second), Pa (Pascal), Nm (Newton meter), and N (Newton).

  • Meter and second are base units, not derived.
  • Pascal is a derived unit (kg/(m·s²)).
  • Newton meter is a derived unit (kg·m²/s²).
  • Newton is a derived unit (kg·m/s²).

B. Pa (Pascal), N (Newton), m/s (meter per second), W (Watt).

  • All of these are derived units. Pascal is kg/(m·s²), Newton is kg·m/s², meter per second is m/s (a derived unit of speed), and Watt is kg·m²/s³.

C. k (kelvin), m (meter), kg (kilogram), s (second).

  • Kelvin, meter, kilogram, and second are all base units, not derived.

D. kg (kilogram), K (kelvin), Pa (Pascal), N (Newton).

  • Kilogram and kelvin are base units, not derived.
  • Pascal and Newton are derived units.

So, the group of derived units is option B: Pa (Pascal), N (Newton), m/s (meter per second), and W (Watt).

This problem has been solved

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